topological space

topological space englannista suomeksi

1. topologinen avaruus

0. Substantiivi

1. topologinen avaruus

topological space englanniksi

1. An pair (''X'', ''τ''), where ''X'' is a set and ''τ'', called the ''topology'', is a collection of subsets of ''X'' which satisfies certain axioms and whose elements are called the ''sets'' (or alternatively, for a different set of axioms, the ''sets''); the set ''X''.

2. {{quote-book|en|year=1964|translator=Jay E. Strum|author=H. J. Kowalsky|title=Topological Spaces|pageurl=https://books.google.com.au/books?id=FLfiBQAAQBAJ&pg=PA165&dq=%22topological+space%22%7C%22topological+spaces%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwi64bTEmbHtAhWBv54KHR1-AYUQ6AEwBnoECDAQAgv=onepage&q=%22topological%20space%22%7C%22topological%20spaces%22&f=false|page=165|publisher=Academic Press

3. 2011, Jonathan A. Barmak, ''Algebraic Topology of Finite Topological Spaces and Applications'', Springer, (w) 2032, page xi,

Most of the spaces studied in Algebraic Topology, such as CW-complexes or manifolds, are Hausdorff. In contrast, finite topological spaces are rarely Hausdorff. A topological space with finitely many points, each of which is closed, must be discrete.

4. {{quote-book|en|year=2013|author=D. J. H. Garling|title=A Course in Mathematical Analysis: Volume 2|pageurl=https://books.google.com.au/books?id=RvMhAwAAQBAJ&pg=PA431&dq=%22topological+space%22%7C%22topological+spaces%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwi64bTEmbHtAhWBv54KHR1-AYUQ6AEwC3oECDsQAgv=onepage&q=%22topological%20space%22%7C%22topological%20spaces%22&f=false|page=431|publisher=Cambridge University Press